Former Labour Party TD Patrick Nulty has dramatically resigned his seat after sending inappropriate message on social media, including one to a 17-year-old girl.

Mr Nulty has only been a TD for just two-and-a-half years after winning the Dublin West by-election following the death of former Finance Minister Brian Lenihan.

The 31-year-old Independent TD said he sent the message to the girl "while under the influence of alcohol". He also said he thinks he has never met the young woman.

Last night, Mr Nulty announced his resignation and appealed for privacy.

"I've made a mistake in my private life and I am taking personal responsibility for it," he told the Irish Independent.

While no official complaint has been made, gardai are now expected to launch a full investigation and interview Mr Nulty.

"Gardai are now examining this case, in light of Mr Nulty's resignation, and will then decide what course of action to pursue," said a senior garda source.

Mr Nulty's immediate resignation came ahead of the revelations of his actions to the Sunday World.

"I sent inappropriate messages via facebook. This included inadvertently sending one to a 17 year old woman. To the best of my knowledge I have never met this woman and the message was sent while under the influence of alcohol," he said.

"I apologise wholeheartedly to the woman involved and to her family. It was never my intention to upset anyone in this way but it was totally wrong," he said in a statement.

After being elected as a Labour TD in October 2011, Mr Nulty resigned from the parliamentary party two months later in protest at the cutbacks in Budget 2012.

He later resigned from the party completely to become an Independent TD, but he remained close to fellow former Labour TDs Roisin Shortall and Tommy Broughan.

Mr Nulty will have to be replaced in a by-election to be held within six months.

The former TD said the message he sent was "entirely inappropriate" and he took full responsibility for his actions.

"For this reason I have decided to resign my seat in the Dail. I set myself the highest standards personally and politically. Unfortunately due to personal mistakes I have not met those standards in this matter and I will take responsibility for that. I still believe passionately that Ireland can be a fairer and more just society based on equality and social justice but at the present time I believe to resign is the correct and right course of action," he said.

Mr Nulty said he would like to extend my deepest thanks and gratitude to all my family, friends and supporters "who have given me so much support over the last five years as a public representative".

"In politics people very often do not take responsibility for their actions. I hope I am doing that. I would further like to apologise to my constituents in Dublin West for my mistake. I hope they will understand my reasons for resigning and accept my apology," he said.

"I hope that as I have taken decisive and direct action on this matter my privacy will now be respected in what has been a very difficult decision for me personally."

Mr Nulty was an outspoken critic of austerity policies. He remained extremely active at a local level following his departure from Labour and had intended to contest the next general election as an Independent candidate.